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Percent of lights

by tritrantran » Sat Dec 06, 2008 11:15 am
Can someone show me how I'm setting this up wrong?

Question:
Eighty percent of the lights at Hotel California are on at 8 p.m. a certain evening. However, forty percent of the lights that are supposed to be off are actually on and ten percent of the lights that are supposed to be on are actually off. What percent of the lights that are on are supposed to be off?

Strategy:
Assume 100 lights, 80 are on, 20 are off.

40% of the 80 Ons are suppose to be off = (80)(.40) = 32

which means 60% of the 80 Ons are suppose to be On = (80)(.6) = 48

10% of the 20 Offs are suppose to be On = (20)(.10) = 2

which means 90% of hte 20 Offs are suppose to be Off = (20)(.9) = 18

Find: What % of lights that are on are supposed to be off?

32/80 = 40% is obviously wrong.

OA [spoiler]10%[/spoiler]
Last edited by tritrantran on Sat Dec 06, 2008 7:03 pm, edited 1 time in total.
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Re: Percent of lights

by Stuart@KaplanGMAT » Sat Dec 06, 2008 11:28 am
tritrantran wrote:Can someone show me how I'm setting this up wrong?

Question:
Eighty percent of the lights at Hotel California are on at 8 p.m. a certain evening. However, forty percent of the lights that are supposed to be off are actually on and ten percent of the lights that are supposed to be on are actually off. What percent of the lights that are on are supposed to be off?

Strategy:
Assume 100 lights, 80 are on, 20 are off.

40% of the 80 Ons are suppose to be off = (80)(.40) = 32
Let's start with this first calculation.

The stem says that "40% of the lights that are supposed to be off are actually on". You didn't apply this statement - instead, you translated this as "40% of the lights that are currently on are supposed to be off", which is completely different. From here stems all your problems.

Picking numbers is a great way to go on this question. Let's use your numbers, since 100 is the perfect choice for a percent question.

100 lights, 80 are on, 20 are off

We know that 40% of the lights that are supposed to be off are on by mistake. Therefore, the lights that are actually off represent 60% of the total number of lights that should be off.

So, 20 = 60%(off)
20 = 3/5(off)
100/3 = off

Well, ok - 100 doesn't work out so well on this question (who knew?). We can live with the fraction, though.

We want the % of lights that are on that should be off.

To calculate the number of lights mistakenly on, we take 40% of 100/3.

(2/5)(100/3) = 40/3

(Note: we could have saved a couple of steps by setting up a ratio to start:

x/20 = 40/60

x = 800/60 = 40/3)

% = part/whole = (40/3)/80 = 40/240 = 1/6 = 16.67%
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by stop@800 » Sat Dec 06, 2008 11:35 am
The qn says
forty percent of the lights that are supposed to be [n]off[/n] are actually on


and you are taking 40% of lights that are supposed to be on

Hope this helps
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by cramya » Sat Dec 06, 2008 12:39 pm
Let T be the total number of lights i.e since problem involves percents let T=100

80%of the lights are on currently i.e 80 lights are on

Let x be the lights that are usually off
Let y be the lights that are usually on

x+y =100 (1)

forty percent of the lights that are supposed to be off are actually on = .40x

ten percent of the lights that are supposed to be on are actually off = .10y

So the number of lights on = forty percent of the lights that are supposed to be off are actually on + 90% of the lights that are usually on
80 = .40x + .90y

i.e 4x+9y=80 (2)

From 1) and 2) x=20(40%OF THIS IS 8) y =80(90%OF THIS IS 72)

(72+8 = 80 gives us the lights taht are on currently)

Percent of the lights that are ON but are supposed to be OFF
= 8/80*100 = 10%


I am getting 10% whats the OA?

Pleas epost OA's using spoiler function if possible.
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by tritrantran » Sat Dec 06, 2008 7:02 pm
Sorry guys here's the OA [spoiler]10%[/spoiler]
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by mental » Sun Dec 07, 2008 6:10 am
The question asks:
What percent of the lights that are on are supposed to be off?

but it also states that:
ten percent of the lights that are supposed to be on are actually off.
isn't this the answer itself???

i used the algebra approach, somewhat similar to cramya's, and eventually arrived at the answer 10%. Well this was the very fact i used in my assumptions and just re-ascertaied it.

was this a coincidence - or the answer was actually disguised in question
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by mental » Sun Dec 07, 2008 6:24 am
Sorry
i dont know what was I thinking :oops:

it is clear now
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by utgolfer » Sun Dec 07, 2008 10:18 am
mental wrote:The question asks:
What percent of the lights that are on are supposed to be off?

but it also states that:
ten percent of the lights that are supposed to be on are actually off.
isn't this the answer itself???

i used the algebra approach, somewhat similar to cramya's, and eventually arrived at the answer 10%. Well this was the very fact i used in my assumptions and just re-ascertaied it.

was this a coincidence - or the answer was actually disguised in question
Is this correct????
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by canuckclint » Wed Dec 10, 2008 1:32 pm
utgolfer wrote:
mental wrote:The question asks:
What percent of the lights that are on are supposed to be off?

but it also states that:
ten percent of the lights that are supposed to be on are actually off.
isn't this the answer itself???

i used the algebra approach, somewhat similar to cramya's, and eventually arrived at the answer 10%. Well this was the very fact i used in my assumptions and just re-ascertaied it.

was this a coincidence - or the answer was actually disguised in question
Is this correct????
Not quite Let soff be suppose to be off.

Question gives:
0.1 * soff = on
.1 = on div soff

What percent of the lights that are on are supposed to be off?
ans = soff div on

Notice its different from above. Just the inverse.

times answer by 100 for pecentage.
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